摘要 為了提升金剛石合成裝備六面頂壓機(jī)頂錘的對(duì)中精度,開展六面頂壓機(jī)鉸鏈梁的工作腔體裝配誤差分析。首先,基于小位移旋量(small displacement torsor,SDT)理論,建立要素采用不同公差原則時(shí)的金剛石壓機(jī)鉸鏈梁裝配公差模型;其次,利用空間矢量表示三維尺寸鏈,基于空間矢量環(huán)疊加原理推導(dǎo)出表示鉸鏈梁活塞頂錘運(yùn)動(dòng)位姿的封閉環(huán)尺寸及其變動(dòng)計(jì)算模型,進(jìn)而得到其底、左、上頂錘中心軸線與各自頂錘外端面交點(diǎn)可能的誤差范圍;最后,比較三維公差分析得到的單個(gè)鉸鏈梁活塞頂錘位姿累積閉環(huán)誤差 FR 與一維尺寸鏈分析得到的類似誤差 X。結(jié)果表明:由于 FR 的組成環(huán)要多于 X 的組成環(huán),其結(jié)果更能準(zhǔn)確地表示鉸鏈梁系統(tǒng)的誤差傳遞結(jié)果,且 FR[?1.005, 1.005] 表示的誤差范圍要大于 X[?1.000, 0.780] 表示的誤差范圍,驗(yàn)證了該方法對(duì)裝配公差分析的優(yōu)越性和準(zhǔn)確性。同時(shí),通過篩選試驗(yàn)設(shè)計(jì)(Plackett-Burman design,PBD)篩選出對(duì)單個(gè)鉸鏈梁活塞頂錘位姿封閉環(huán)影響較顯著的變量,為合理分配壓機(jī)鉸鏈梁的加工精度提供了理論基礎(chǔ),有利于保障金剛石壓機(jī)頂錘的對(duì)中精度,合理分配壓機(jī)鉸鏈梁相關(guān)結(jié)構(gòu)配合公差及各部件的容差,并優(yōu)化設(shè)備的加工成本。
關(guān)鍵詞 金剛石合成壓機(jī);鉸鏈梁;對(duì)中精度;公差原則;三維公差
中圖分類號(hào) TH6; TQ164 文獻(xiàn)標(biāo)志碼 A
文章編號(hào) 1006-852X(2024)06-0733-11
DOI 碼 10.13394/j.cnki.jgszz.2023.0202
收稿日期 2023-09-20 修回日期 2023-12-28
中國的金剛石人工合成設(shè)備以鉸鏈?zhǔn)搅骓攭簷C(jī)(簡(jiǎn)稱“六面頂壓機(jī)”)為主[1] 。隨著壓機(jī)大型化步伐加快,其性能得到較大提升,同時(shí)也對(duì)壓機(jī)裝配精度提出了更高的要求。由于金剛石主要在頂錘接觸形成的正六面體腔體中生長(zhǎng),頂錘的對(duì)中誤差很大程度上影響著六面頂壓機(jī)合成金剛石的效率和品質(zhì)。如果鉸鏈梁等相關(guān)部件公差設(shè)計(jì)不合理,不僅難以得到生產(chǎn)高品質(zhì)、大顆粒金剛石的工作腔,還會(huì)導(dǎo)致六面頂壓機(jī)裝配困難,生產(chǎn)效能低下。目前,常用的一維、二維尺寸鏈分析方法無法準(zhǔn)確計(jì)算六面頂壓機(jī)鉸鏈梁系統(tǒng)誤差的傳遞和累計(jì)[2] 。
目前的公差分析正在逐步向三維空間轉(zhuǎn)變,公差圖模型、雅可比旋量模型、矢量模型、小位移旋量模型等是比較流行的三維公差分析模型[3-6] 。任彥松等 [7]用二維矢量環(huán)法和計(jì)算機(jī)輔助的統(tǒng)計(jì)分析法對(duì)折疊舵面的尺寸鏈進(jìn)行了分析,通過對(duì)比兩者所得各相關(guān)尺寸的敏感度和貢獻(xiàn)度指標(biāo)吻合程度,驗(yàn)證了矢量環(huán)法的可靠性。對(duì)于復(fù)雜的裝配體,二維模型并不能完整表達(dá)其裝配誤差,而三維模型分析方法則更具優(yōu)勢(shì)[8] 。熊峰等[9]基于雅可比旋量,建立了復(fù)雜裝配體的三維公差分析模型,其分析結(jié)果更有準(zhǔn)確性。DENIS 等[10]運(yùn)用 SDT 方法,將微小偏量用旋轉(zhuǎn)矢量及位移矢量代替,使公差區(qū)域的邊界得到了充分的處理。穆曉凱等[11]在考慮幾何公差的基礎(chǔ)上加入了裝配載荷作用下零件變形的影響,構(gòu)建了實(shí)際裝備的綜合三維數(shù)學(xué)模型,該方法使機(jī)械系統(tǒng)在工作過程中的可靠性與穩(wěn)定性得到一定程度的保證。周志鵬等[12]提出了一種考慮公差原則影響的統(tǒng)計(jì)公差分析方法,并結(jié)合蒙特卡羅模擬技術(shù)實(shí)現(xiàn)了機(jī)械裝配的統(tǒng)計(jì)公差分析。孟巧鳳等[13]利用三維公差分析軟件開展了裝備裝配過程仿真,獲得的公差優(yōu)化方案兼顧了產(chǎn)品的裝配需求及零件成本。
為了系統(tǒng)研究六面頂壓機(jī)鉸鏈梁各環(huán)節(jié)誤差的傳遞和累計(jì),針對(duì)目前公差分析大都未考慮公差原則的影響等問題,在對(duì)六面頂壓機(jī)工作腔體的裝配誤差進(jìn)行分析時(shí),考慮公差原則的影響。首先,基于 SDT 理論分別建立要素遵循不同公差原則的六面頂壓機(jī)鉸鏈梁三維公差 SDT 模型;然后,基于空間矢量環(huán)疊加原理,推導(dǎo)六面頂壓機(jī)鉸鏈梁尺寸鏈的三維公差分析模型,進(jìn)而得到底、左、上頂錘中心軸線可能的變動(dòng)范圍;進(jìn)一步地將三維公差分析模型得到的左鉸鏈梁中心軸線在 Z 向的變動(dòng)范圍與一維尺寸鏈的分析結(jié)果進(jìn)行對(duì)比;最后,通過 PBD 篩選出對(duì)封閉環(huán)影響較顯著的變量,以期為合理分配壓機(jī)鉸鏈梁的加工精度提供理論基礎(chǔ)。
1""""公差分析中的三維公差模型
以 SDT 理論為基礎(chǔ)建立不同公差原則下的三維公差模型。
1.1""""公差區(qū)域的 SDT 模型
3.2 " "底鉸鏈梁三維公差分析
(x 0 ,y 0 , z 0 )由于每個(gè)鉸鏈梁的構(gòu)型都是一樣的,參考上述左鉸鏈梁工作部件的尺寸精度分析,可得在原始坐標(biāo)系下,底鉸鏈梁活塞頂錘軸線與頂錘外端面交點(diǎn)的 位 置 誤 差 變 動(dòng) 為: X、 Y 向 , [?0.030, 0.055]; Z 向 ,[?0.080, 0.100](單位 mm)。
3.3 " "上鉸鏈梁三維公差分析
圖 5 為底、左、上鉸鏈梁裝配簡(jiǎn)圖。與前面的分析方法類似,將上鉸鏈梁的活塞桿及其相關(guān)零部件固連為一個(gè)整體,則如圖 5 所示的裝配體的裝配要求是活塞頂錘軸線與頂錘外端面交點(diǎn)相對(duì)于基礎(chǔ)坐標(biāo)系的位置誤差。由于不同鉸鏈梁的形狀、形位公差是一樣的,參考圖 3 中各功能要素間的裝配關(guān)系,假設(shè)要素采用包容原則,根據(jù)前述的內(nèi)容進(jìn)行建模并計(jì)算,可得在左鉸鏈梁、銷軸的影響下,上鉸鏈梁活塞孔軸相對(duì)于原始坐標(biāo)系可能的位置誤差變動(dòng)為:Z 向,[?0.885,0.835];X 向,[?0.040, 0.040];Y 向,[?0.575,0.555](單位mm)。
結(jié)合前面的結(jié)論,可得上鉸鏈梁液壓缸活塞頂錘軸線與頂錘外端面交點(diǎn)相對(duì)于基礎(chǔ)坐標(biāo)系可能的位置誤差變動(dòng)為:X 向,[?0.111, 0.135];Y 向,[?1.180, 1.155];Z 向,[?1.820, 1.915](單位 mm)。
由上述結(jié)論可得,液壓缸活塞頂錘軸線與頂錘外端面交點(diǎn)的可能位置誤差示意圖圖 6。如圖 6 所示:坐標(biāo)系 為理想對(duì)中坐標(biāo)系,坐標(biāo)系的原點(diǎn)為理想的活塞頂錘軸線對(duì)中點(diǎn)。由于各頂錘軸線方向上的誤差可以由活塞運(yùn)動(dòng)彌補(bǔ),所以各頂錘在運(yùn)動(dòng)軸線方向上的誤差不再進(jìn)行贅述。對(duì)于鉸鏈梁液壓缸活塞頂錘軸線與頂錘外端面交點(diǎn)的誤差,可認(rèn)為其構(gòu)成一個(gè)可能的變動(dòng)區(qū)域,該區(qū)域中各特征點(diǎn)的坐標(biāo)分別為:
d 1 (?0.030,0.055,?35.000),
d 2 (0.055,0.055,?35.000),
d 3 (0.055,?0.030,?35.000),
d 4 (?0.030,?0.055,?35.000),
b 1 (?0.070,?35.000,1.035),
b 2 (?0.070,?35.000,?0.855),
b 3 (0.095,?35.000,?0.855),
b 4 (0.095,?35.000,1.035),
c 1 (0.135,1.155,35.000),
c 2 (0.135,?1.180,35.000),
c 3 (?0.111,?1.180,35.000),
c 4 (?0.111,1.155,35.000)。
4 " "鉸鏈梁裝配結(jié)構(gòu)不同公差分析方法結(jié)果對(duì)比
一維尺寸鏈分析是公差分析中常用的方法。以前述的左鉸鏈梁液壓缸軸線在 Z 方向上的累積閉環(huán)誤差尺寸 FR 變動(dòng) X 為封閉環(huán),構(gòu)建如圖 7 所示的一維尺寸鏈,其中:尺寸 為底鉸鏈梁銷軸孔中心到底鉸鏈梁底面的垂直尺寸, 為左鉸鏈梁銷軸孔中心到左鉸鏈梁活塞孔軸線的垂直尺寸,平行度 、垂直度 為增環(huán),銷軸孔配合間隙 B 1 、B 2 和銷軸直線度 M 2 為減環(huán)。
(1)對(duì)圖 7 的尺寸鏈用極值法分析可得變動(dòng) X為 [?1.000, 0.780](單位 mm)。
(2)采用蒙特卡羅方法分析,并用 Matlab 編程進(jìn)行仿真計(jì)算[17] 。假設(shè)圖 7 的尺寸鏈各組成環(huán)的公差帶為正態(tài)分布,在給定的組成環(huán)公差域內(nèi)取值,采用蒙特卡羅方法進(jìn)行 50 000 次仿真計(jì)算,可得封閉環(huán)變動(dòng) X為 [?0.930, 0.410](單位 mm)。
采用 2 種公差模型計(jì)算的結(jié)果如表 3 所示。從表 3可以看出:在實(shí)際裝配過程中,由于配合間隙以及形位公差的存在,銷軸孔軸實(shí)際接觸位置不確定,運(yùn)用三維分析方法獨(dú)立原則計(jì)算出的變化范圍比一維尺寸鏈極值法的范圍更大,更能反映真實(shí)裝配環(huán)境的不確定性。在對(duì)一維尺寸鏈采用蒙特卡羅方法計(jì)算時(shí),其結(jié)果小于極值法計(jì)算的結(jié)果,這是由于在計(jì)算時(shí)假設(shè)各零件的公差遵循正態(tài)分布,更符合實(shí)際生產(chǎn)狀況,所以其也更加接近實(shí)際裝配誤差。同理也可對(duì)表 2 中 SDT 模型中各矢量的變動(dòng)特性采用蒙特卡羅方法進(jìn)行分析計(jì)算,這里不再贅述。
5 " "鉸鏈梁裝配結(jié)構(gòu)變量公差水平顯著性分析
選取表2中a1~a10的公差N1~N10為設(shè)計(jì)變量,以 表2中組成環(huán)a1~a10的公差域?yàn)閰⒖?,選取變量的低 水平和高水平,得到表4的PBD變量水平表和各變量 的對(duì)應(yīng)編碼。
根據(jù)表4中的數(shù)據(jù),利用軟件Design-expert進(jìn)行PBD試驗(yàn)表設(shè)計(jì);在考慮包容要求時(shí),用上文所述的三 維差分析模型分別進(jìn)行計(jì)算,得到每組試驗(yàn)的封閉環(huán) FR(i=1,2,3,…,12)數(shù)值,如表5所示。通過Design-ex- pert軟件對(duì)表5中的數(shù)據(jù)進(jìn)行分析,得到回歸分析表。
在分析時(shí)發(fā)現(xiàn)N2、N。對(duì)結(jié)果影響非常小,且N2、N。的存在會(huì)影響模型整體的收斂效果,為避免不顯著參數(shù) 對(duì)模型造成干擾,剔除N4(對(duì)應(yīng)尺寸a4)、N。(對(duì)應(yīng)尺 寸a6)。各參數(shù)的回歸分析結(jié)果如表6所示,主要考 察表6中的p值,p值越小,代表變量對(duì)響應(yīng)的影響越 大;當(dāng)plt;0.0500時(shí),代表其影響顯著;當(dāng)plt;0.0100時(shí), 代表其影響高度顯著。
由表6可知,編碼A、B、E、G對(duì)應(yīng)的變量高度顯著,即變量N,對(duì)應(yīng)的平行度公差、變量N2對(duì)應(yīng)的尺寸公差、N3與N,對(duì)應(yīng)的直線度公差對(duì)封閉環(huán)的影響遠(yuǎn)遠(yuǎn) 高于其他幾個(gè)變量。因此,在鉸鏈梁的設(shè)計(jì)階段應(yīng)嚴(yán) 格要求這4個(gè)公差的大小,以保證鉸鏈梁頂錘對(duì)中精 度的準(zhǔn)確性。
6結(jié)論
基于SDT理論對(duì)六面頂壓機(jī)建立了不同公差原 則下的三維公差分析方法,通過該方法分別計(jì)算出了 底、左、上鉸鏈梁頂錘軸線可能的誤差變動(dòng)范圍。通 過對(duì)比三維分析方法得到的累積閉環(huán)誤差FR[-1.005, 1.005](單位mm)與一維尺寸鏈法得到的誤差 XI-1.000,0.780](單位mm),發(fā)現(xiàn)前者的誤差范圍要 大于后者的誤差范圍,這也證明本研究所使用的三維 分析模型方法要優(yōu)于一維公差分析方法。同時(shí),在采 用不同的公差原則進(jìn)行計(jì)算分析時(shí),包容原則對(duì)應(yīng)的誤差范圍 [?0.855, 0.980](單位 mm)要小于獨(dú)立原則對(duì)應(yīng)的誤差范圍 [?1.005, ?1.005](單位 mm),即在應(yīng)用包容原則時(shí)可能的位置誤差變動(dòng)更小,更符合對(duì)金剛石六面頂壓機(jī)頂錘高精度對(duì)中的要求。最后通過PBD 篩選出了對(duì)封閉環(huán)影響較顯著的變量,為合理分配壓機(jī)鉸鏈梁的加工精度提供了理論基礎(chǔ)。
在后續(xù)的工作中,將考慮壓機(jī)結(jié)構(gòu)在工作中的形變,研究其對(duì)位姿精度的影響。進(jìn)一步地在保證壓機(jī)對(duì)中精度的條件下,開展零件公差的優(yōu)化分配。
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作者簡(jiǎn)介
王良文,男,1963年生,教授、博士生導(dǎo)師。主要研究方向:仿生機(jī)器人、機(jī)器人機(jī)械學(xué)、智能裝備。
E-mail: w_liangwen@sina.com
(編輯:周萬里)
Analysis"of"anvil"centering"accuracy"of"cubic"press"based"on"small
displacement"torsor"theory
WANG Liangwen
1 , DONG Sijie 1 , SI Liang 2 , WANG Shuguang 3 , XIE Guizhong 1 ,
DU Wenliao
1 , LI Ke 4 , LU Haixia 2
(1. Henan International Joint Laboratory of Complex Mechanical Equipment Intelligent Monitoring and Control,
College of Mechanical and Electrical Engineering, Zhengzhou University of Light Industry,
Zhengzhou 450002, China)
(2. Zhongyuan Critical Metals Laboratory, School of Material Science and Engineering,
Zhengzhou University, Zhengzhou 450001, China)
(3. Henan Huanghe Whirlwind Co., Ltd., Changge 461500, Henan, China)
(4. Henan Huanghe Tanaka Keme Press Co., Ltd., Changge 461500, Henan, China)
Abstract " "Objectives: The diamond synthetic equipment in China is mainly the hinged cubic press (referred to as cu-bic press). With the acceleration of large-scale presses, the performance of cubic presses has greatly improved, but high-er requirements have also been put forward for the assembly accuracy of these presses. In order to improve the center-ing accuracy of the top hammer of the cubic press, the assembly errors of the working cavity of the hinge beam for thecubic press are researched. Methods: Firstly, based on the small displacement torsor (SDT) theory, the assembly toler-ance model of the hinge beam of the cubic press with different tolerance principles is established. Secondly, the spacevector is used to represent the three-dimensional dimension chain. Based on the space vector ring superposition prin-ciple, the closed ring size and its variation calculation model representing the motion posture of the hinge beam pistontop hammer is derived, and the possible error range of the intersection points between the bottom, the left, and the uppertop hammer axes and their respective top hammer outer end faces are obtained. Finally, the cumulative closed-loop er-ror FR obtained from the three-dimensional tolerance analysis of the single hinge beam piston top hammer posture iscompared with the similar error X 1 obtained from the one-dimensional dimensional chain analysis. At the same time, thePlackett-Burman design (PBD) is used to screen out the variables that have a significant effect on the sealing ring of thetop hammer posture of a single hinge beam piston. Results: (1) Through the calculation of the three-dimensional toler-ance analysis method established by the cubic press, it is found that the possible errors of the axis of the top hammer ofthe left hinge beam are [?0.070, 0.095] in the X direction, [?0.655, 0.655] in the Y direction, and [?0.855, 1.035] in the Zdirection. The possible errors of the axis of the top hammer of the bottom hinge beam are [?0.030, 0.055] in the X and Ydirections, and [0.080, 0.100] in the Z direction. The possible errors of the axis of the top hammer of the upper hingebeam are [?0.111, 0.135] in the X direction, [?1.180, 1.155] in the Y direction, and [?1.820, 1.915] in the Z direction.(2) The dimensional variation error X 1 of the hydraulic cylinder axis of the left hinge beam in the Z direction is com-pared and calculated by using the one-dimensional dimensional chain. The variation error X 1 of the closed ring is[?1.000, 0.780] when the dimensional chain extreme value method is used for analysis, and the variation error X 1 of theclosed ring is [?0.930, 0.410] when the Monte Carlo method is used for analysis. The calculated result of the MonteCarlo method is less than that of the extreme value method. This is because the calculation assumes that the tolerancesof each part follow a normal distribution, which is more in line with the actual production situation and closer to the ac-tual assembly error. (3) When the diameter of the pin adopts the principle of independence, the possible position error ofthe size of the hydraulic cylinder axis of the left hinge beam in the Z direction is [?1.005, 1.005]. When the diameter ofthe pin is marked by the inclusion principle, the position error changes to [?0.855, 0.980]. From the comparison of res-ults, the use of different tolerance principles leads to different tolerance analysis results. (4) The Plackett-Burman design(PBD) is used to screen out four highly significant variables, namely, the parallelism tolerance corresponding to vari-able M 1 , the dimensional tolerance corresponding to variable M 2 , and the straightness tolerance corresponding to vari-ables M 5 and M 7 , which have a great impact on the precision of the hinge beam. Conclusions: Based on SDT theory, thethree-dimensional tolerance analysis method under different tolerance principles is established for the cubic press, andthe possible error variation ranges of the bottom, left and upper hinge beam top hammer axes are calculated respectively.By comparing the errors obtained by the three-dimensional analysis method with those obtained by the one-dimensionaldimensional chain method, it is found that the former has a larger error range than the latter, which proves that the three-dimensional analysis model method used in this paper is superior to the one-dimensional tolerance analysis method. Atthe same time, when the pin diameter is marked with different tolerance principles, the axis error of the hinge beam hy-draulic cylinder is calculated, and the error range corresponding to the inclusion principle is smaller than that corres-ponding to the independent principle. That is to say, when the inclusion principle is applied in the pin diameter marking,the position variation error of the hinge beam hydraulic cylinder axis can be ensured to be smaller, which is more in linewith the high-precision requirements of the diamond cubic press. Finally, the four highly significant variables that havegreat influence on the precision of the hinge beam are selected, providing a theoretical basis for the reasonable distribu-tion of the machining precision of the press hinge beam.
Key words " "diamond synthesis press;hinge beam;centering accuracy;tolerance principle;three-dimensional tolerance